If I use this card's [All Turns] effect to place a card under a Tamer with cards under it, in what order do I place the card?

Can I change the stacking order of face-down cards under a Tamer?

Can I search/look at face-down cards under a Tamer?

What happens if a face-down card under a Tamer is trashed?

When I place multiple cards from the top of my deck face down under a Tamer without looking at them, in what order do I place them?

2 copies of this card are in the battle area. When my Option card with the [Glowing Dawn] trait would be used, can I activate the [Your Turn] effects on both copies of this card and reduce the cost by a total of 2?